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n 19-22, find (a) a cosine function and (b) a sine function whose graph matches the given curve. Explain. 20. AY (0, 1) AV 19. (0, 3) (2, -3) 4

n 19-22, find (a) a cosine function and (b) a sine function whose graph matches the given curve. Explain. 20. AY (0, 1) AV 19. (0, 3) (2, -3) 4

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Instruction:** In problems 19-22, find (a) a cosine function and (b) a sine function whose graph matches the given curve. Explain. **Graphs Description:** **19.** - The graph is a cosine wave starting at the point (0, 3) with a peak. - The curve intersects the x-axis at \( \frac{\pi}{4} \) and descends to its minimum at \( \frac{3\pi}{4} \). **20.** - The graph is a sine wave starting from the origin (0, 1). - It goes beneath the x-axis reaching its lowest point at (2, -3). **21.** - The graph shows a transformed cosine wave. - The peak is at \( \left(\frac{9}{2}, 3\right) \) and the point (2, 1) appears before it, indicating a phase shift. **22.** - The sine wave starts at \( \left(-\frac{\pi}{3}, -1\right) \). - It achieves a peak at \( \left(\frac{2\pi}{3}, 1\right) \). Each image represents trigonometric functions with transformations such as vertical shifts, horizontal shifts, reflections, and changes in amplitude and period. The goal is to match cosine and sine functions to these graphs.
Transcribed Image Text:**Instruction:** In problems 19-22, find (a) a cosine function and (b) a sine function whose graph matches the given curve. Explain. **Graphs Description:** **19.** - The graph is a cosine wave starting at the point (0, 3) with a peak. - The curve intersects the x-axis at \( \frac{\pi}{4} \) and descends to its minimum at \( \frac{3\pi}{4} \). **20.** - The graph is a sine wave starting from the origin (0, 1). - It goes beneath the x-axis reaching its lowest point at (2, -3). **21.** - The graph shows a transformed cosine wave. - The peak is at \( \left(\frac{9}{2}, 3\right) \) and the point (2, 1) appears before it, indicating a phase shift. **22.** - The sine wave starts at \( \left(-\frac{\pi}{3}, -1\right) \). - It achieves a peak at \( \left(\frac{2\pi}{3}, 1\right) \). Each image represents trigonometric functions with transformations such as vertical shifts, horizontal shifts, reflections, and changes in amplitude and period. The goal is to match cosine and sine functions to these graphs.
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